Geotechnical Engineering

DHARM

ELEMENTS OF SOIL DYNAMICS AND MACHINE FOUNDATIONS 859

Passive isolation is also called ‘motion or amplitude isolation’, since the attempt here is
to reduce the motion or amplitude of the machine (which may affect its performance) induced
by ground vibration caused by disturbing sources in the vicinity.

k c

P sin tz w

M

P sin tz w

Machine

Isolator

FoundatonFoundaton

(a) Schematic for active isolation (b) Mathematical model for active isolation

Fig. 20.32 Active type of vibration isolation

Machine

Z = A sin tw Isolator k c

M

z = A sin tw

FoundationFoundation

(a) Schematic for passive isolation (b) Mathematical model for passive isolation
Fig. 20.33 Passive type of vibration isolation
The term “Transmissibility” is defined in the case of active isolation as the ratio of force
transmitted to the foundation to the vibratory force developed by the machine itself. In the
case of passive type of isolation, the term is defined as the ratio of the amplitude of the sensi-
tive machine to the amplitude of the base.

A common expression for transmissibility, T, can be derived for both these cases from
the theory of vibration:

T =

()

()

14

14

22

22 2 2

+

−+

D

D

ξ

ξξ

...(Eq. 20.113)

where ξ is frequency ratio and D is the damping factor. If the damping is very small, a simpler
expression for transmissibility can be used:

T =

1

1 2

2

()( )−ξ =^22 −

f

ff

n

n

...(Eq. 20.114)